The device, which is understood to have been live, was found in a skip by a worker as he was sorting through rubbish at just before noon.
The tip was quickly evacuated along with most of the surrounding businesses in Arun Business Park as police cordoned off the area.
A bomb disposal squad from the Royal Logistical Corps arrived and carried out an investigation.
They decided to detonate the device on site, and had to clear a number of cars that were parked nearby.
Afterwards one of the experts stated that the object was a fin stabilized artillery shell, a long-range, modern shell that is fired out of a large gun.
It was thought to be live and did contain some explosives, the expert said.
It is not known how the shell arrived in the skip.